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   <h4 class="subsectionHead"><span class="titlemark">2.10   </span> <a 
 id="x15-560002.10"></a>Free warping analysis elements</h4>
<!--l. 1364--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">2.10.1   </span> <a 
 id="x15-570002.10.1"></a>TrWarp</h5>
<!--l. 1365--><p class="noindent" >Implements 2D linear triangular three-node finite element for <span 
class="cmtt-10">FreeWarping </span>analysis. Each node has
1 degree of freedom. The node numbering is anti-clockwise. The element features are summarized in
Table&#x00A0;<a 
href="#x15-5700143">43<!--tex4ht:ref: TrWarpsummary --></a>.
<div class="center" 
>
<!--l. 1369--><p class="noindent" >
<div class="table">
<!--l. 1369--><p class="noindent" ><a 
 id="x15-5700143"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-44" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-44-1g"><col 
id="TBL-44-1"></colgroup><colgroup id="TBL-44-2g"><col 
id="TBL-44-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-44-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-44-1-2"  
class="td11"><!--l. 1369--><p class="noindent" ><span 
class="cmbx-10">TrWarp</span>                                                         </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-44-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-44-2-2"  
class="td11"><!--l. 1369--><p class="noindent" >2D linear triangular warping element                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-44-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-44-3-2"  
class="td11"><!--l. 1369--><p class="noindent" >-                                                                            </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-44-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-4-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-44-4-2"  
class="td11"><!--l. 1370--><p class="noindent" >One dof (the value of deplanation function) is required in
each node.                                                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-44-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-5-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-44-5-2"  
class="td11"><!--l. 1371--><p class="noindent" >Linear approximation of displacements and geometry.      </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-44-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-6-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-44-6-2"  
class="td11"><!--l. 1372--><p class="noindent" >Integration using one point gauss integration formula.      </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-44-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-7-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-44-7-2"  
class="td11"><!--l. 1373--><p class="noindent" >This type of element is supported in <span 
class="cmtt-10">FreeWarping </span>analysis
only.                                                                       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-44-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-8-1"  
class="td11">CS properties       </td><td  style="white-space:wrap; text-align:left;" id="TBL-44-8-2"  
class="td11"><!--l. 1374--><p class="noindent" >Only <span 
class="cmtt-10">warpingCS </span>is supported.                                     </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-44-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-9-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-44-9-2"  
class="td11"><!--l. 1375--><p class="noindent" >Edge  loads  corresponding  to  free  warping  problem  are
generated  automatically.  Additional  edge  loads  are  not
supported.                                                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-44-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-10-1"  
class="td11">Nlgeo                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-44-10-2"  
class="td11"><!--l. 1376--><p class="noindent" >0.                                                                          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-44-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-11-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-44-11-2"  
class="td11"><!--l. 1377--><p class="noindent" >-                                                                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-44-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-12-1"  
class="td11">Note                   </td><td  style="white-space:wrap; text-align:left;" id="TBL-44-12-2"  
class="td11"><!--l. 1378--><p class="noindent" >Test case: sm/freewarpingtest2.in                                 </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-44-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-13-1"  
class="td11">                </td></tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-44-14-"><td  style="white-space:nowrap; text-align:left;" id="TBL-44-14-1"  
class="td11"></td></tr></table>
</div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;43: </span><span  
class="content">TrWarp element summary</span></div><!--tex4ht:label?: x15-5700143 -->
</div><hr class="endfloat" />
</div>
</div>
                                                                                           
                                                                                           
                                                                                           
                                                                                           
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